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The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

 Jun 1, 2024
 #1
avatar+129487 
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The average will be    2^n / (n + 1)   where n is the row number =  0,1,2,3........

 

So

 

2^(n )  / (n + 1) =  2

 

2^(n)  = 2(n + 1)

 

From inspection, we can determine that  n  =   3 

 

            1

      1        1

   1      2        1

1     3       3       1   →    3td  row

 

 

cool cool cool

 Jun 1, 2024

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